1、1 IntroductionThe colorimetric characteristics of television component color signals are determined by three separate sets ofparameters. They are:a) Color primaries and reference white: These characteristics are specified by CIE colorimetric parametersand define the relationship between scene color
2、and the linear RGB video signals. The primaries also definethe maximum gamut of color that can be transmitted with all-positive RGB signals.b) Opto-electronic transfer characteristics (gamma) used to derive the RGB gamma-corrected signals fromthe linear RGB values.c) The luminance equation and the c
3、olor channel coding matrix derived using that luminance equation. Thiscoding matrix defines the relationship between the gamma corrected RGB values and the component colorsignals Y PB PR (analog) or Y CB CR (digital).In current practice, the differences between the first two colorimetric characteris
4、tics are small and can usually beignored. This guideline is concerned only with the third of these characteristics and assumes the first two to beidentical. The analog and digital cases are treated separately because their color-difference gains differ slightly.2 ScopeExisting television interface s
5、tandards utilize at least two different color channel coding matrices to derivetheir corresponding analog Y PB PR or digital Y CB CR component color signals. Clearly, it will be necessaryto perform transformations between these color component signal sets. This guideline describes the derivationof t
6、he transformation matrices and lists example transformations between color component signals adoptingITU-R BT.601 (see note 1) and ITU-R BT.709 (HD-CIF and 1125/60 see note 2) luma/chroma equations for boththe digital and analog component signal sets. A parametric form of conversion matrix is derive
7、d for convertingbetween signal sets with arbitrary source and target luma coefficients.3 Derivation of transform matricesA general form of the transform matrix for converting between arbitrary sets of luma/chroma coefficients is nowderived.3.1 Luma equationsThe derivation starts with luma equations
8、(1) and (2) for the source and target systems:EG 36-2000SMPTE ENGINEERING GUIDELINEApproved March 23, 2000Copyright 2000 by theSOCIETY OF MOTION PICTURE AND TELEVISION ENGINEERS595 W. Hartsdale Ave., White Plains, NY 10607(914) 761-1100Transformations Between TelevisionComponent Color SignalsPage 1
9、of 7 pagesEYS= YRS ER+ YGS EG+ YBS EB(1)EYT= YRT ER+ YGT EG+ YBT EB(2)where YRS, YGS, and YBSare the source set of coefficients, and YRT, YGT, and YBTare the target set. Usingthese coefficients, along with the required chroma scalings, separate coding matrices and the final source-to-targettransform
10、 matrices are derived for the analog and digital component cases.3.2 Analog derivationSubscripted E variables, used for the analog representation, represent gamma-corrected component signals inthe source and target luma equation sets. For EY, ER, EG, and EB, black is at 0 and white at 1.0. EPBandEPR
11、have 100% color ranges of 1/2 to +1/2. (Alternatively, the ranges could have been chosen to representthe common analog range, 0-700 mV for EY, ER, EG, and EB, and 350 mV for EPBand EPR.)AMTX signifies the coding matrix used for analog component transformations (DMTX is used later for thecorrespondin
12、g digital component transformations).The conversion from the source to target luma/chroma equations is performed in equations (3)-(5). The sourcecomponent signal is first converted to ERS, EGS, and EBS, by multiplying it by the inverse coding matrix for thesource signal:EREGEBs= AMTXs1 EYEPBEPRs(3)P
13、remultiplying both sides of equation (3) by the target coding matrix, AMTXT, and assuming that the ER, EGand EBvalues for the source and target sets are identical, yieldsEYEPBEPRT= AMTX StoT EYEPBEPRs= AMTX T AMTX S 1 EYEPBEPRS(4)with the overall conversion from the source to target beingAMTX StoT =
14、 AMTX T AMTX S 1(5)Essentially, the source component has been decoded back to RGB using the source luma coefficients and thenreencoded to the target component signal using the forward matrix for the target luma coefficients.3.3 Digital representationFor the component digital treatment, subscripted D
15、 variables are used, and all coding and transform matricesbegin with the letter D. The digital representation uses the component definitions of ITU-R BT.601 which arecommonly used in many subsequent digital video standards. The differences between the digital and analogcases are that The digital DR,
16、 DG, DB, and DY, and DCBand DCRhave different peak-to-peak signal levelsof 2192n-8and 2242n-8, where n 8, respectively, whereas in the analog case treated here, thetwo ranges are the same. This causes the transform matrices to be scaled differently, by the factor224/219, in a few of the terms. DR, D
17、G, DB, and DYhave black-and-white reference levels of 162n-8and 2352n-8respectively, andEG 36-2000 Page 2 of 7 pages DCBand DCRare in offset binary form, with offsets of 1282n-8where n 8.The integer n would be 8 or 10 for most of the digital video formats, but some applications might use highervalue
18、s.The correspondence between the digital D variables and corresponding analog E variables is given byDRDGDB= INT (219 ER+ 16) 2 n8(219 EG+ 16) 2 n8(219 EB+ 16) 2 n8DYDCBDCR= INT (219 EY+ 16) 2 n8(224 EPB+ 128) 2 n8(224 EPR+ 128) 2 n8(6)where the INT operator returns the nearest integer.3.4 Source-to
19、-target component digital transformation matrixThe derivation for component digital signals is the same as for the analog case except for the differentrepresentation. The respective inverse and forward codings are expressed asDRDGDBS= INT DMTX S 1 DYDCB128 2n8DCR128 2n8s(7)andDYDCBDCRT= INT DMTX T D
20、RDGDBT+ 0 128 2n8128 2n8(8)As in the analog equations (3)-(5), the overall conversion matrix is expressed as:DYDCBDCRT= INT DMTX StoT DYDCB128 2n8DCR128 2n8s+ 0 128 2n8128 2n8(9)where the overall source to target transformation isDMTX StoT= DMTX T DMTX S1(10)3.5 General parametric form for coding an
21、d decoding matricesThe conversion matrices in the clause above can be derived by algebraic manipulation from the source and targetequations (1) and (2). A single matrix, MTX, is used for both the analog and digital cases with the different chromascalings accounted for with the factor , which could b
22、e either 1 or 224/219. MTX should read AMTX using =1 for the analog case, and DMTX using = 224/219 for the digital case.The inverse coding matrix for the source luma coefficient set isEG 36-2000Page 3 of 7 pagesMTX S1= 1 0 2(1YRS) 11 Y BS 2(1Y BS)Y GS 1 Y RS 2(1Y RS)Y GS) 11 2(1YBS) 10 (11 )The forw
23、ard coding matrix for the target set isMTX T= YRTYRT2(1 YBT) 2YGTYGT2(1 YBT) YGT2(1 YRT) YBT2YBT2(1 YRT) (12) The overall conversion matrix, below, from source to target is obtained by manually multiplying equations(11) and (12) together:MTX StoT= 1 YBT YGT YBSYGS 2(1 YBS) 1YRT YGT YRSYGS 2(1 YRS) 1
24、0 YGT YBSYGS 2(1 YBT)+ 12 2(1 YBS) YGT YRSYGS YRT 2(1 YRS)2(1 YBT)0 YGT YBSYGS YBT 2(1 YBS)2(1 YRT)YGT YRSYGS 2(1 YRT)+ 12 2(1 YRS)(13)Factors of two are maintained in some places in the equations above to maintain the similarity with the numericalform in equations (16) to (19) below.4 Numerically e
25、xact matrices for converting between ITU-R BT.601 and BT.709The conversion matrices are provided in exact numerical form for converting between the ITU-R BT.601 andITU-R BT.709 luma/chroma equation sets in equations (14) and (15), respectively.EY 601= 0.299 ER+ 0.587 EG+ 0.114 EB (14)EY 709= 0.2126
26、ER+ 0.7152 EG+ 0.0722 EB (15)This exact form of expression can then be used to derive a matrix of whatever lesser precision is needed for agiven application. Even though the luma coefficients may be provided to only 3 or 4 significant figures of precision,having higher precision in the other rows of
27、 the matrix can be useful for ensuring higher overall accuracy and bettergenerational fidelity.EG 36-2000 Page 4 of 7 pages4.1 AnalogAMTX709 to 601= = 1 0.114 0.587 0.07220.7152 1.8556 0.299 0.587 0.21260.7152 1.5748 0 0.587 0.07220.7152 1.772+ 0.5 1.8556 0.587 0.21260.7152 0.299 1.57481.7720 0.587
28、0.07220.7152 0.114 1.85561.4020.587 0.21260.7152 1.402+ 0.5 1.5748(16)AMTX601 to 709= 1 0.0722 0.7152 0.1140.587 1.772 0.2126 0.7152 0.2990.587 1.402 0 0.7152 0.1140.587 1.8556+ 0.5 1.772 0.7152 0.2990.587 0.2126 1.4021.85560 0.7152 0.1140.587 0.0722 1.7721.57480.7152 0.2990.587 1.5748+ 0.5 1.402(17
29、)4.2 DigitalDMTX709 to 601= = 1 0.114 0.587 0.07220.7152 1.8556 2192240.299 0.587 0.21260.7152 1.5748 2192240 0.587 0.07220.7152 1.772+ 0.5 1.8556 0.587 0.21260.7152 0.299 1.57481.7720 0.587 0.07220.7152 0.114 1.85561.4020.587 0.21260.7152 1.402+ 0.5 1.5748(18)DMTX601 to 709= 1 0.0722 0.7152 0.1140.
30、587 1.772 2192240.2126 0.7152 0.2990.587 1.402 2192240 0.7152 0.1140.587 1.8556+ 0.5 1.772 0.7152 0.2990.587 0.2126 1.4021.85560 0.7152 0.1140.587 0.0722 1.7721.57480.7152 0.2990.587 1.5748+ 0.5 1.402(19)EG 36-2000Page 5 of 7 pages5 Transform matrices calculated to eight decimal placesFor convenienc
31、e, the matrices are provided below in numerical form to a precision of eight decimal places usingordinary rounding. An implementer may take these values and reduce the precision to that which is desired fora given application. If the application has a critical accuracy requirement, such as generatio
32、nal fidelity, roundingto the lower precision may be carried out as described in clause 6.5.1 Analog (to eight decimal places)AMTX 709to601= 1 0 00.10157905 0.98985381 0.072452960.19607625 0.11065251 0.98339782 (20)AMTX 601to709= 1 0 0 0.11818787 1.01863972 0.07504945 0.21268507 0.11461795 1.02532707
33、 (21)5.2 Digital (to eight decimal places)DMTX 709to601= 1 0 00.09931166 0.98985381 0.072452960.19169955 0.11065251 0.98339782 (22)DMTX 601to709= 1 0 0 0.11554975 1.01863972 0.07504945 0.20793764 0.11461795 1.02532707 (23)6 Rounding of matrix coefficientsFor a given precision requirement, ordinary r
34、ounding is not always the best way to obtain accurate values. Onereason is that the rounded value of a sum of three real numbers is not always equal to the sum of the individuallyrounded numbers. Consequently, the unity normalization of the Y-row sum, or zero normalizations in thecolor-difference ro
35、w sums, might be thrown off by a count in either direction. A simple method ofaccomplishing the rounding is to first do ordinary rounding; then, if a desired row normalization is notcorrect, nudge the matrix element that is nearest to its corresponding real value either up or down toaccomplish the d
36、esired normalization.A more comprehensive method is presented in ITU-R BT.1361, annex 2, wherein a least-squares optimizationmethod is applied to each row to determine an optimal set of coefficients. Also, part of the ITU-R BT.1361procedure is a means whereby the optimization can be performed over a
37、 subregion of the RGB space.NOTES1 ITU-R BT.601 has no specification of primaries or transfer characteristics. It specifies only the third coding-matrix part ofthe colorimetric characteristics. The ITU-R BT.601 coding matrix is based on the color primaries and the reference white ofthe NTSC (1953) s
38、pecification which is practically no longer used. The equation is also used in SMPTE 170M, EBU 625standards, and the 1250/50 (1152 active lines) specification of ITU-R BT.709, ITU-R BT.1358, and ANSI/SMPTE 293M.2 In ITU-R BT.709, which includes the 1920 1080 common image format (HD-CIF), the unified
39、 colorimetric parameters arespecified for HD-CIF regardless of 1125/60 and 1250/50. These unified colorimetric parameters are identical with thosespecified for 1125/60 and those described in ITU-R BT.1361. The equation is also used in SMPTE 274M, ANSI/SMPTE295M, and ANSI/SMPTE 296M.EG 36-2000 Page 6
40、 of 7 pagesAnnex A (Informative)Luma equations used by some television scanning standardsTable A.1 gives luma equations used by some television scanning standards.Annex B (informative)BibliographyANSI/SMPTE 293M-1996, Television 720 483 Active Line at 59.94-Hz Progressive Scan Production Digital Rep
41、re-sentationANSI/SMPTE 295M-1997, Television 1920 1080 50 Hz Scanning and InterfacesANSI/SMPTE 296M-1997, Television 1280 720 Scanning, Analog and Digital Representation and Analog InterfaceSMPTE 170M-1999, Television Composite Analog Video Signal NTSC for Studio ApplicationsSMPTE 240M-1999, Televis
42、ion 1125-Line High-Definition Production Systems Signal Parameters SMPTE 274M-1998, Television 1920 1080 Scanning and Analog and Parallel Digital Interfaces for Multiple Picture RatesITU-R BT.601-5 (10/95), Studio Encoding Parameters of Digital Television for Standard 4:3 and Wide-Screen 16:9 Aspect
43、RatiosITU-R BT.709-3 (02/98), Parameter Values for the HDTV Standards for Production and International Programme ExchangeITU-R BT.1358 (02/98), Studio Parameters of 625 and 525 Line Progressive Scan Television SystemsITU-R BT.1361 (02/98), Worldwide Unified Colorimetry and Related Characteristics of
44、 Future Television and Imaging SystemsTelevision Luma equationScanning standard ITU-R BT.601 ITU-R BT.709 OtherSMPTE 170MNTSCXEBU 625PAL, SECAMXANSI/SMPTE 293M525 / 720 483 / 59.94 / 1:1XSMPTE 274M1125 / 1920 1080 / multiple rates / 1:1, 2:1XANSI/SMPTE 295M1250 / 1920 1080 / 50 / 1:1, 2:1XANSI/SMPTE
45、 296M750 / 1280 720 / multiple rates / 1:1XSMPTE 240M1125 / 1920 1035 / 60, 59.94 / 2:1SMPTE 240M(see note)NOTE ANSI/SMPTE 240M uses a luma equation that is similar to ITU-R BT.709 but is not exactly the same.In many applications, the differences may be small enough to ignore, but these differences could becomesignificant in critical applications.Table A.1 Luma equationsEG 36-2000Page 7 of 7 pages
